Complex Voltage and Current
In order to simplify calculations, sinusoidal voltage and current waves are commonly represented as complex-valued functions of time denoted as and .
Impedance is defined as the ratio of these quantities.
Substituting these into Ohm's law we have
Noting that this must hold for all, we may equate the magnitudes and phases to obtain
The magnitude equation is the familiar Ohm's law applied to the voltage and current amplitudes, while the second equation defines the phase relationship.
Read more about this topic: Electrical Impedance
... A phasor is a constant complex number, usually expressed in exponential form, representing the complex amplitude (magnitude and phase) of a sinusoidal function of time ... can be defined as the ratio of the phasor voltage across the element to the phasor current through the element, as determined by the relative amplitudes and phases of ...
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